Answer to Question #306176 in Algebra for suve

Question

find all trees T where two-thirds of the vertices of T have degree 1 and the remaining one-third of the vertices have degree 3

Answer 1

For the total of Tress T

The sum of degree of vertices tree is= 2n-2 so let n be the number of vertices and the unkown N= 3/2+ x

2( 2/3+ x) -2 = x +( 1/31)+(2×3)+(2×x)

4x

: 6x/3x-2= x+ 2x+ 1 + 18/3

2x - 3x= 19/3+2

-x = 25/3 ...therefore x= - 8 (1/3)